Upwind and High-Resolution Schemes

ISBN-13: 9783642644528 / Angielski / Miękka / 2011 / 588 str.

M. Yousuff Hussaini; Bram Van Leer; John Van Rosendale

Opis

One of the major achievements in computational fluid dynamics has been the development of numerical methods for simulating compressible flows, combining higher-order accuracy in smooth regions with a sharp, oscillation-free representation of embedded shocks methods and now known as "high-resolution schemes". Together with introductions from the editors written from the modern vantage point this volume collects in one place many of the most significant papers in the development of high-resolution schemes as occured at ICASE.

Spis treści

ICASE and the History of High-Resolution Schemes.- ICASE and the History of High-Resolution Schemes.- A Brief Introduction to High-Resolution Schemes.- A Brief Introduction to High-Resolution Schemes.- I. Riemann Solvers and Upwind Schemes.- Annotation.- 1. On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist—Osher and Roe.- 2. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws.- 3. Flux-Vector Splitting for the Euler Equation.- II. Second-Order Total-Variation Diminishing Schemes.- Annotation.- 1. A Comparative Study of Computational Methods in Cosmic Gas Dynamics.- 2. High Resolution Schemes and the Entropy Condition.- 3. Convergence of Generalized MUSCL Schemes.- 4. A Simplified TVD Finite Difference Scheme Via Artificial Viscosity.- 5. On Central-Difference and Upwind Schemes.- III. Essentially Non-oscillatory Schemes.- Annotation.- 1. Uniformly High-Order Accurate Nonoscillatory Schemes. I.- 2. Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III.- 3. ENO Schemes with Subcell Resolution.- 4. Efficient Implementation of Essentially Non-oscillatory Shock-Capturing Schemes, II.- 5. Essentially Nonoscillatory Spectral Fourier Methods for Shock Wave Calculations.- 6. Cell Averaging Chebyshev Methods for Hyperbolic Problems.- IV. Multidimensional Schemes.- Annotation.- 1. A Rotationally Biased Upwind Difference Scheme for the Euler Equations.- 2. Discrete Models for the Numerical Analysis of Time-Dependent Multidimensional Gas Dynamics.- 3. Discontinuous Solutions to Hyperbolic Systems Under Operator Splitting.- 4. High Resolution Finite Volume Methods on Arbitrary Grids Via Wave Propagation.- 5. Design of an Essentially Nonoscillatory Reconstruction Procedure on Finite-Element-Type Meshes.- 6. A Contribution to the Great Riemann Solver Debate.- 7. An Approximate Riemann Solver for Magnetohydrodynamics (That Works in More Than One Dimension).- Papers Reprinted.

Blurb

One of the major achievements in computational fluid dynamics has been the development of numerical methods for simulating compressible flows. These methods combine higher-order accuracy in smooth regions, with sharp, oscillation-free representation of embedded shocks, and are now known as "high-resolution schemes". This volume collects in one place many of the most significant papers in the development of high-resolution schemes as occurred at ICASE, together with introductions from the editors, written from the modern vantage point. Chapter I covers the early development of approximate Riemann solvers in the context of monotonic schemes. Chapter II continues with papers dealing with second-order total-variation-diminishing (TVD) schemes. Chapter III presents papers which show the historical development of total-variation-bounded (TVB) schemes at ICASE. Finally, Chapter IV collects papers on inherently multidimensional schemes, which preserve the attractive features of their one-dimensional predecessors.